Faithful representation: 15.5
Faithfully (group acting): 12.10
Farey series: 13.14, prob. 3
Fatou's lemma: 13.5
Filter base: 12.3, prob. 6
Finer covering: 12.6
Finer partition: 13.9, prob. 7
Finer topology: 12.1
Finite real-valued function: 12.7
Fischer-Riesz theorem: 13.11
Flight vector: 12.15, prob. 11
Frechet space: 12.14
Freely (group acting): 12.10
Fuglede's theorem: 15.11, prob. 2
Fundamental sequence of partitions: 13.9,
prob. 7
Fundamental system of bounded subsets in
a topological vector space: 12.14,
prob. 9
G-covering, -packing, -tessellation: 14.1,
prob. 6
Gauss-Kuzmin formula: 13.14, prob. 4
Gelfand transformation: 15.3
Gelfand-Mazur theorem: 15.2
Gelfand-Neumark theorem: 15.4
Gleason part: 15.3, prob. 18
Group algebra: 14.7
Group of real numbers modulo 1: 14.2
Group with no small subgroups: 12.9,
prob. 6
H
Haar measure: 14.1
Hahn-Banach theorem: 12.15, prob. 4
Half-space: 12.14, prob. 11
Hamburger's moment problem: 13.20,
prob. 5
Hardy-Littlewood maximal function: 15.10,
prob. 5
Hardy spaces: 15.3, prob. 15, 16
Hardy's inequality: 13.11, prob. 13
Hausdorff space: 12.3
HausdorfTs moment problem: 13.4, prob.
11
Hermitian character: 15.4, prob. 3 and 15.9
Hermitian element (in an algebra with
involution): 15.4
Hermitian unbounded operator: 15.13
Hilbert algebra: 15.7
Hilbert form: 15.6
Hilbert sum of representations: 15.5
Hilbert-Schmidt operator: 15.4
Holder's inequality: 13.11, prob. 12
Homogeneous space: 12.11
Hopfs maximal ergodic theorem: 13.11,
prob. 16
Hyperextremal measure: 15.3, prob. 11
I
Identity component of a topological group:
12.8
Image of a measure: 13.1 and 13.4, prob. 8
Incompressible mapping: 13.9, prob. 11
Index of an operator: 15.11, prob. 22 and
15.12, prob. 3
Induced measure: 13.1 and 13.9
Induced topology: 12.2
Inequality of the mean: 13.8, prob. 14
Infinite matrix: 15.4
Information: 13.9, prob. 27
Inner measure of a set: 13.5
Integrable function, set: 13.7
Integral of an integrable function: 13.1 and
13.7
Integral of a function over a set A: 13.9
Integral with respect to a complex measure:
13.16
Integration by parts: 13.21, prob. 6
Interior function: 15.3, prob. 12
Invariant measure (on a group): 14.1
Involution in an algebra: 15.4
Irreducible idempotent: 15.8
Isometric isomorphism of normed algebras:
15.1
Isomorphism of topological groups: 12.8
Isomorphism of topological vector spaces:
12.13
Isoperimetric inequality: 14.3, prob. 10
J
Jacobi matrix: 15.13, prob. 1
Jacob's theorem: 12.15, prob. 11
Jensen measure: 15.3, prob. 9on: 13.11, prob.